@Kha I was tired of writing `arbitrary _` :)
There 0 places in the stdlib where the type needs to be provided.
If in the future we need to specify the type we can use
`arbitrary (α := <type>)`
@Kha `withReader` is a well-behaved version of `adaptReader`. `adaptReader` is
too general, and it often produces counterintuitive elaboration
errors.
Here are two super annoying issues I hit all the time:
1- `adaptReader` + polymorphic code
```
def ex1 : ReaderT Nat IO Unit :=
adaptReader (fun x => x + 1) $
IO.println "foo" -- 3 Errors here failed to synthesize `Monad ?m` and `MonadIO ?m`, and don't know how to synthesize `Type → Type`
```
2- `adaptReader` and notation that requires the expected type
```
structure Context :=
(x y : Nat)
def ex2 : ReaderT Context IO Nat :=
adaptReader (fun s => { s with x := 10 }) $ -- Error at the structure instance
...
```
In the example above, I have to write `fun (s : Context) => ...` to
fix the problem.
The two problems above happen in the old and new frontends. However,
there is a new problem specific for the new frontend. In the new
frontend, a `do` is only elaborated when the expected type is known.
So, `adaptReader (fun ctx => ...) do ...` seldom works :(
As I said above, the issue is that `adaptReader` is too general. Its
type is
```
{ρ ρ' : Type u_1} → {m m' : Type u_1 → Type u_2} → [MonadReaderAdapter ρ ρ' m m'] → {α : Type u_1} → (ρ' → ρ) → m α → m' α
```
`withReader` is a simpler version of `adaptReader`
```
withReader : {ρ : Type u_1} → {m : Type u_1 → Type u_2} → [MonadWithReader ρ m] → {α : Type u_1} → (ρ → ρ) → m α → m α
```
It doesn't have any of the problems above. Moreover, I managed to replace
every single instance of `adaptReader` with `withReader` at the stdlib
and tests. We don't need the `adaptReader` generality.
@Kha this is a little bit ugly. As in Lean3, the notation `{ }` is
overloaded. It can be `HasEmptyc.emptyc` or the empty structure.
Moreover, if we have an instance `HasEmptyc A` for a structure `A`,
then `{ }` is notation for `HasEmptyc.emptyc`. I am not very happy
about this, but it seems users use this feature. It is even used in
our own Lean4 code base :)
BTW, I will try a different alternative later.
First, move the notation `{ }` as a proper parser for `emptyc`.
Then, make sure the elaborator throws an error when
`{ }` is ambiguous. That is, `{}` can be elaborated as the empty
structure `A` and there is an `HasEmptyc A` instance.
Example:
```
structure A :=
(x : Nat := 0)
instance : HasEmptyc A :=
⟨{ x := 10 }⟩
```
The main issue here is that the support for choice+postpone is
currently broken.
